An optimal isolation policy for an epidemic

Abstract

Policies of isolating infectives in the general stochastic epidemic are considered. With costs assigned to the infection and isolation of individuals, an optimal policy is found, which at any stage minimises the expected future cost. An optimal policy is also found for the general deterministic epidemic and the two policies are compared. Finally, some numerical examples are provided.

Optimal intervention strategies for an epidemic: A household view

“…Dynamic programming is a common solution technique in these analytic methods. Abakuks [45][46][47] considered the cost of infection, isolation among infectives, and immunization of susceptibles in a discrete-time general stochastic epidemic to find optimal isolation and immunization polices which result in the minimum expected future cost. Abakuks also provided the optimal policy for the deterministic model for each case.…”

“…Abakuks also provided the optimal policy for the deterministic model for each case. Clancy 48 extended the results of Abakuks [45][46][47] to epidemic models with more general infection and removal rate functions and more complicated isolation and immunization costs. Clancy provided sufficient conditions on infection and removal rates in order for the optimal policies to have the same simple form as the general stochastic epidemic.…”

Optimal impulse control of a SIR epidemic

“…Impulse control means that at any time it is possible, for a certain price, to reduce instantly the number of susceptibles (case of vaccination) or infectives (case of isolation). Such models, the case of isolation, were investigated in other works . Roughly speaking, the optimal strategy prescribes to isolate all the infectives at once, as soon as the number of infectives is below a certain threshold.…”

“…Impulse control of various dynamical systems attracts the attention of many researchers, eg, those in other works to mention the most relevant and the most recent works. The underlying system can be described in terms of ordinary or stochastic differential equations. In other works, along with the given deterministic drift, there are spontaneous (or natural) Markov jumps of the state.…”

“…Then, restarting at this new point, the process runs until the next intervention and so on. Sometimes, such control is called “singular control.” The goal is to minimize the total (expected) accumulated cost, which may be discounted or not . The popular method of attack to such problems is dynamic programming .…”